In recent years, direct-sequence (DS) code division multiple access (CDMA) spread spectrum communication systems and methods experience growing attention worldwide. The IS-95 cellular communication standard is one example for application of DS-CDMA communications, which are described in TIA/EIA/IS-95-A, "Mobile Station-Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System," Feb. 27, 1996.
Other implementations of CDMA can be found in third generation cellular systems, wireless multimedia systems, personal satellite mobile systems, and more. The basic principle of direct sequence code division multiple access communications, is that each user is assigned with a distinct spreading code, which is often referred to as a pseudo noise (PN) sequence. The spreading code bits (also called chips), are used to modulate the user data. The number of chips used to modulate one data symbol is known as the spreading factor (processing gain) of the system, and it is related to the spreading in bandwidth between the (unmodulated) user data and the CDMA signal.
In its simplest form, the base-band equivalent of the transmitted CDMA signal is, ##EQU1##
where SF is the spreading factor, .left brkt-bot./SF.right brkt-bot. denotes the integer part of n/SF, a.sub.i [.left brkt-bot.n/SF.right brkt-bot.] and PN.sub.i [n] are the data symbol and spreading code of the i-th user, respectively, and K is the number of active users. Note that by the definition of .left brkt-bot.n/SF.right brkt-bot., a.sub.i [.left brkt-bot.n/SF.right brkt-bot.] is fixed for SF consecutive chips, in accordance with the definition above that each data symbol is modulated by SF chips. PA1 where R[n] denotes the received signal after down conversion and sampling and "*" denotes the complex conjugation. For simplicity we assume QPSK signaling in Equation 2. A simplistic example is provided, by setting K=2 (i.e. a system which includes two users) and discarding channel degradation (i.e. R[n]=T[n]). Hence, the following expression is obtained by substituting Equation 1 into Equation 2, EQU y.sub.1 [m]=a.sub.1 [m]+CrossCorr.sub.1,2 [m].multidot.a.sub.2 [m] Equation 3 PA1 where ##EQU3## PA1 Yoshida, "CDMA-AIC highly spectrum Efficient CDMA cellular system based on adaptive interference cancellation", IEICE transactions on communication v e79-b n Mar. 3, 1996, p. 353-360, PA1 A. Yoon, "A Spread spectrum multi-access system with co-channel interference cancellation", IEEE journal of selected areas in communications, September 1993, PA1 U.S. Pat. No. 5,105,435 to Stilwell, entitled "Method And Apparatus For Canceling Spread Spectrum Noise", and PA1 Y. Li, "Serial interference cancellation method for CDMA" electronics letters, September 1994. PA1 H. V. Poor and X. Wang, "Code aided interference suppression for DS/CDMA communications: Interference suppression capability", IEEE Tran. On Comm, September 1997. PA1 H. V. Poor and X. Wang, "Code aided interference suppression for DS/CDMA communications: Parallel Blind Adaptive Implementations", IEEE Tran. On Comm, September 1997. PA1 where Y[i].sub.k is the i-th sample of the k-th rake receiver. PA1 receiving a portion of the signal, where the portion is modulated by a predetermined section of the cyclic sequence, PA1 receiving an additional portion of the signal, where the additional portion is modulated by the same predetermined section of the cyclic sequence, PA1 jointly processing the portion and the additional portion, and PA1 producing a set of receiver parameters, which minimize a predetermined cost function for the predetermined section of the cyclic sequence. PA1 demodulating the signal, by the cyclic sequence, thereby producing a plurality of received samples, PA1 determining a plurality of sections, each section having a length of at least one sample, each the section being demodulated by a predetermined portion of the cyclic sequence, PA1 detecting portions of the demodulated signal, which are associated with each of the sections, PA1 jointly processing the detected portions, which are associated by a selected one of the sections, and PA1 producing a set of receiver parameters for each the sections, the receiver parameters minimizing a predetermined cost function for the selected section.
If T.sub.S and T.sub.C denote the symbol and chip intervals in seconds, respectively, then T.sub.S =SF.multidot.T.sub.C. The chip rate is defined as 1/T.sub.C, and the symbol rate is defined as 1/T.sub.S. Accordingly, the chip rate is SF times greater than the symbol rate.
In a DS-CDMA system, all of the users are continuously transmitting over the same frequency band. Thus, at the receiver end, each user is distinguishable from all other users, only through his spreading code. The spreading codes are therefore designed to minimize cross-talk effects between the different users. Conventional systems often use orthogonal spreading sequences.
In practice, however, channel distortions and asynchronicity modify the transmitted signals, and as a consequence, cross-talks between the users exist even when orthogonal spreading codes are utilized by the transmitter.
A plurality of receiver structures are known in the art for DS-CDMA signals, including single-user (SU) and multi-user (MU) receivers, interference cancellation (IC) receivers, and more.
A conventional single-user receiver correlates the received signal with the spreading code of the desired user (user no. 1), as follows ##EQU2##
The term CrossCorr.sub.1,2 [m].multidot.a.sub.2 [m] in Equation 3 denotes the interference caused to user 1 by user 2. This simple example reveals a well known weakness of the SU receiver, namely, its performance is governed by the noise level induced by the cross-talk from all other channel users (see for example, A. J. Viterbi, "CDMA Principals of Spread Spectrum Communication", Addison-Wesley Publishing Company, 1995). A more advanced SU receiver includes some means of interference cancellation, which are aimed at reducing these cross-talks, and improving the receiver's performance. For example, see the following references:
Multi-user (MU) receivers jointly demodulate several or all of the received signals associated with the currently active users. The structure of MU receivers is much more complicated than that of SU receivers, but their performance is significantly better since these receivers are less sensitive to cross-talks between the users. (see for example, S. Verdu "Multi-user Detection" Cambridge University Press, 1998, and the references therein).
In practice, the communication link between the transmitter and the receiver is often time varying. Therefore, the CDMA receiver, which can be an SU, MU or IC receiver, is required to be adaptive, thereby being capable of tracking the time variations of the communication channel. See for example U.S. Pat. No. 5,572,552 to Dent et. al, entitled "Method and system for demodulation of down-link CDMA signals". See also, G. Woodward and B. S. Vucetic, "Adaptive Detection for DS-CDMA," Proceedings of the IEEE, Vol 86, No. 7 July 1998.
Adaptive algorithms, like those available for DS-CDMA applications, are designed to minimize the expectation of a predetermined cost function (preferably a convex one) with respect to the receiver's parameters. For example, S. Verdu, "Adaptive Multi-User Detection", Proc. IEEE Int. Symp. On Spread Spectrum Theory and Applications, (Oulu Finland, July 1994), is directed to an adaptive least-mean-squares (LMS) MU algorithm which minimizes the mean squared error between the transmitted and reconstructed symbols, i.e. EQU MSE.sub.i.tbd.E{(a.sub.i [n]-a.sub.i [n]).sup.2 } Equation 5
where a.sub.i [n] are the MU receiver output samples at the i-th terminal, and a.sub.i [n] are the transmitted symbols of the i-th user. The cost function in Equation 5 requires training sequences. In other words, the receiver must know the exact value of at least some of the transmitted symbols (the a.sub.i [n]'s) in order to minimize this cost.
Other methods, which are known in the art, do not require training data. S. Verdu, "Adaptive Multi-User Detection", Proc. IEEE Int. Symp. On Spread Spectrum Theory and Applications, (Oulu Finland, July 1994), is also directed to such a method. This method encompasses a decision directed approach, which replaces the unknown a.sub.i [n]'s by estimation values thereof.
In the binary case, for example, a.sub.i [n] accepts only two levels: "1" and "-1". Thus, an estimate of a.sub.i [n] can be obtained from the sign of the corresponding receiver outputs. In this case, the cost in Equation 5 reduces to EQU E{(a.sub.i [n]-Sign{a.sub.i [n]}).sup.2 } Equation 6
Another method known in the art is described in M. Honig, U Madhows and S. Verdu, "Blind Adaptive Multi-User Detection, IEEE Trans. on Information Theory, July 1995. This reference is directed to a method which is based on the fact that under certain conditions, the cost in Equation 5 is equivalent to the following cost EQU OE.sub.i.tbd.E{a.sub.i [n].sup.2 } Equation 7
in the sense that the minimization of these two different cost functions yields the same receiver.
Since the criterion in Equation 7 does not involve the a.sub.i [n]'s, there is no need for a training sequence. The cost in Equation 7 is known as the minimum output energy (MOE) cost, since the receiver is updated so that the energy at its outputs is minimized. The resulting MOE adaptive algorithms are referred to as "blind" multi-user algorithms, since they operate "blindly" without knowing the transmitted bits.
It is often convenient to express the cost function in terms of sample averaging instead of stochastic expectations. For example, the MSE cost can be defined, at time instant as follows: ##EQU4##
where 0&lt;.lambda..ltoreq.1 is an exponential forgetting factor giving more weight to recent samples than to previous ones, thus allowing tracking capabilities.
The following references are directed to an adaptive recursive least squares (RLS) type algorithm for the minimization of this criterion:
Similar algorithms can be derived for the cost function in Equation 7, by re-writing it in the following form ##EQU5##
Reference is now made to FIG. 1A, which is a schematic illustration of a system for adaptive detection of a DS-CDMA signal, generally referenced 80, which is known in the art. System 80 is basically a processing unit, which implements any of the above methods. The received samples y[1],y[2], . . . , y[m], are provided as input to the processor. The processor, implementing any of the above methods, calculates the adaptation parameters .theta.[m] for minimizing the cost function which characterizes the receiver 80.
It would be obvious to someone skilled in the art, that the received samples y[1],y[2], . . . , y[m] may also be vector valued, e.g. the outputs from a bank of SU receivers each tuned to a different user.
Reference is now made to FIG. 1B which is a schematic illustration of a bank of rake receivers, known in the art. It is noted that a rake receiver is a single user (SU) receiver.
Section 50 includes an array 52 of rake receivers and a processor 56, connected thereto. The array 52 includes a plurality of rake receivers 54A, 54B, 54C and 54M, which are set to receive the signals of as much as M users.
The input samples to the processor 56 are vector valued in this case, so that each sample Y[i] is given by ##EQU6##
The embodiment in FIG. 1B is often utilized in adaptive MU receivers where the processor 56 can detect the transmitted information of user 1 by processing the samples provider by rake receiver 54A, while taking into consideration the influence of the respective samples of the second user, as provided by the second rake receiver (54B), the respective samples of the third user, as provided by the third rake receiver (54C) and so forth.
Adaptive algorithms are often conveniently described in terms of their bandwidth. An adaptive algorithm is considered to have an overall response of a low-pass filter due to the inherent averaging operation that is either implicitly or explicitly dominant in any adaptive scheme. The bandwidth of this equivalent low-pass response is considerably lower than that of the data, and it governs the tracking and noise rejection capabilities of the adaptive algorithm. A large bandwidth implies fast tracking but relatively high residual noise (i.e. large error variance of .theta.[m], whereas low bandwidth implies good noise rejection but poor tracking capabilities.
In many DS-CDMA systems, the spreading code is much longer than the symbol period (the down-link of IS-95 systems, for example). Adaptive algorithms, like the ones reported in the above references, whose bandwidth is lower than the symbol rate, are inappropriate for such systems. This is due to the fact that these algorithms are unable to track the fast varying interference between the users (whose bandwidth is proportional to the symbol rate since a new interference value is produced with each new data symbol). The reason for the fast varying nature of the interference lies in the fact that when the PN sequence spans more than one data symbol, different portions of the PN sequence are utilized in Equation 4 with different data symbols. Thus, the cross-correlation accepts a different value with each new data symbol.
In some cases, this situation is unavoidable, (e.g. when random spreading codes are utilized). However, in most cases of practical interest, the spreading codes are non-random and finite.